Crab crossing in inverse Compton scattering

Inverse Compton scattering is a promising x-ray source, very bright, quasi-monochromatic, and compact. In this paper, we present a generalized theory of Compton backscattering in terms of luminosity, suitable for both classical and quantum regimes. We show that the optimal parameters, which require a certain mutual orientation and inclination of the fronts of the laser and electron beams described by 3D Gaussians, correspond to the crab scheme. This scheme is widely used in particle physics but is not yet used for x-ray sources. The constructed theory not only predicts the optimal geometry for laser and electron beams but also describes the luminosity. Our results reveal the opportunity to sharply increase the luminosity of compact x-ray sources based on Compton/Thomson backscattering.